Few Christians read the psalms as messianic prophecies, but that's what many of them are.
After they had set a day to meet with him [Paul], they came to him at his lodgings in great numbers. From morning until evening he explained the matter to them, testifying to the kingdom of God and trying to convince them about Jesus both from the law of Moses and from the prophets. (Acts 28:23–24)
In several of our last podcasts, we implored our listeners to see the Old Testament in a new light, as setting forth the story and witness of God's Messiah. In this light, we can easily see types and shadows of Jesus in the stories of Joseph, Jonah, and even Job. And, amazingly, we even hear the echoes of him in the Psalms. Now, some might think we're coming out of left field on this, but consider what Richard B. Hays, Duke Divinity School Dean, says about the psalms in his book, The Conversion of the Imagination.
The passages surveyed here draw from a select group of the "psalms of David" (Pss 18; 22; 31; 40; 42; 69) that describe the unjust suffering of the righteous king and celebrate the hope, or experience, of God's deliverance of the sufferer. Furthermore, every one of these psalms is introduced in the LXX [Septuagint, the Greek translation of the Old Testament] by the enigmatic superscription εις τελος. . . . Whatever this superscription may have meant originally, it is not hard to see how early Christian interpreters, reading the LXX, might have understood it as a hermeneutical instruction to construe these texts eschatologically. —Richard B. Hays, The Conversion of the Imagination
In other words, Christians living in the first century read many of David's psalms as Jesus' own voice. WOOT!